Fitting ellipsoids to objects by the first order polarization tensor

This article present the manual to determine ellipsoids that has the same first order polarization tensor to any conducting objects included in electrical field. Given the first order polarization tensor for an object at specified conductivity, the analytical formula of the first order polarization tensor for ellipsoid in the integral form is firstly expressed as system of nonlinear equation by the trapezium rule. We will then discuss how the derived equations are simultaneously solved by appropriated numerical method to uniquely compute all semi principal axes of the ellipsoid. Few examples to use the proposed technique in this study are also provided in three different situations. In each case, the first order polarization tensor for the obtained ellipsoid can be calculated back from the analytical formula to examine the effectiveness of the method.